01 - Trim the root just enough so each onion stands upright while staying intact. Peel the outer skin. Make 4 to 6 vertical cuts from the top down toward the root, stopping about ¼ inch from the base to keep the layers connected. Rotate the onion and add additional cuts to form 8 to 12 evenly spaced petals. Gently fan the petals apart with your fingers.
02 - Combine the flour, cornstarch, smoked paprika, garlic powder, onion powder, salt, black pepper, and cayenne in a shallow bowl. In a separate bowl, whisk together the eggs and milk until uniform.
03 - Dredge each onion in the dry flour mixture, turning to coat all petals thoroughly. Shake off the loose excess, then submerge in the egg-milk wash. Transfer back to the dry mixture and press gently to ensure every petal is evenly breaded.
04 - Pour vegetable oil into a deep pot or fryer and heat to 350°F.
05 - Lower one or two onions into the oil cut-side down. Fry for 2 to 3 minutes until golden, then flip and continue frying for another 2 to 3 minutes until crisp and cooked through.
06 - Lift the onions out with a slotted spoon and set them on paper towels to drain. Sprinkle lightly with additional salt if desired.
07 - Stir together the mayonnaise, ketchup, prepared horseradish, smoked paprika, garlic powder, lemon juice, and a pinch of salt in a bowl until well combined.
08 - Arrange the hot mini bloomin onions on a serving plate alongside the dipping sauce.